To put it succinctly...
Too many places?
OMG yes. And I move fast. Even as someone who goes faster than most people here think is wise, I think your original plan is wildly unrealistic. Sorry.
Hint: A sure sign that you are slicing things too thinly is when you start seeing yourself plan days that are all split up, like "morning in X, drive to Y and have lunch, evening in Z" - I know because I do this (and fight the urges) all too often myself. Down, boy...
A hard truth: Your trip is 10 days. You can not count your arrival or departure days. And the day after you arrive you will be jet-laggged and probably only at 50% of yourself. With 9.5 actual days, you need to be ruthless. Nine days is a trip to France, not to Scandinavia, Germany, Netherlands, and France.
As I read your priorities, you want: Normandy & WWI sites, Chateaux of the Loire, and Paris. With about 9 days, there's your trip right there. Copenhagen? What are you thinking? Hamburg? Fuggedaboudit. Amsterdam? Doubtful (although technically possible, if you are very, very efficient everywhere).
Call me crazy if you want, but...here's how you fix this:
Fly in to Paris, spend a day or two there. PIck up your rental car (on the outskirts of the city, it's a very stressful place to drive).
Head out to Bayeaux, Normandy sites, maybe Mont St Michel (not far away). Spend a couple days across this area.
Head to the Loire Valley to get your chateaux fix (needs 1-2 days).
Drop your car in the Loire and train back to Paris for a couple days before flying home.
If you can arrange every stop with split-second timing and Swiss-watch efficiency, maybe, MAYBE you could hop a train to Amsterdam for a day before flying home from there. Do not forget to factor in the time it takes to get from point A to point B, plus time lost every time you move (check out, navigate, get lost, eat, get lost, find your way, check in, eat, etc.).
That is a beautiful trip (and still very hurried), to some of Europe's most wonderful places and experiences. You'll love it. Save the other places for a future trip. They'll still be there next time.
Driving exclusively in France also removes that painful $200 drop-off fee for your rental car.
Just my 2 eurocents. Hope this helps.